The mother, a 30-year-old Korean woman, arrived at the hospital late on Monday night last week and the baby was born early the following morning.

Ms Goward said police and the Department of Family and Community Services had failed in their attempts to find the baby's mother.

The baby has been temporarily called Ahn, which is a common Korean surname, and is in the care of foster parents in Sydney. He is said to be in good health and Ms Goward described him as a "beautiful baby".

Hospital staff reported that it appeared the mother and baby had bonded in hospital. Ms Goward said this provided some hope the mother may want to come forward.

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"The mother stayed with the baby for the day and left about 5 o'clock. We have exhausted all our own avenues," she said. "We would certainly like to see the baby and the mother reunited."

Ms Goward said the mother had nothing to fear from the Department of Community Services and was not in trouble. She wanted to contact the mother to work out the best options for the long-term care of the baby.